Question

plot \\(\frac{9}{10}\\) and \\(2\frac{4}{5}\\) on the number line below.

Explanation:

Step1: Analyze the number line

The number line has marks from 0 to 3, with each integer (0, 1, 2, 3) and the space between them divided into equal parts. First, find the length of each small segment. Between 0 and 1, let's see how many segments there are. From 0 to 1, if we count the ticks, let's assume the number of segments between 0 and 1 is \( n \). Let's check the fraction \( \frac{9}{10} \) and \( 2\frac{4}{5} \).

Step2: Plot \( \frac{9}{10} \)

\( \frac{9}{10} \) is less than 1. The number line between 0 and 1: let's find the division. If we consider that from 0 to 1, the number of small ticks (excluding 0 and 1) is, say, 9 (since \( \frac{9}{10} \) is 9 tenths). Wait, looking at the number line, between 0 and 1, how many segments? Let's count the spaces. From 0 to 1, there are 10 small segments (since 0 to 1 is 1 unit, divided into 10 parts, each part is \( \frac{1}{10} \)). So each small segment is \( \frac{1}{10} \). So \( \frac{9}{10} \) is 9 segments from 0, so we plot it 9 ticks to the right of 0 (before 1).

Step3: Convert \( 2\frac{4}{5} \) to tenths

\( 2\frac{4}{5} = 2 + \frac{4}{5} \). Convert \( \frac{4}{5} \) to tenths: \( \frac{4}{5} = \frac{4\times2}{5\times2} = \frac{8}{10} \). So \( 2\frac{4}{5} = 2 + \frac{8}{10} = 2\frac{8}{10} \). Now, between 2 and 3, the number line is also divided into 10 segments (each \( \frac{1}{10} \)). So from 2, we move 8 segments to the right (since \( \frac{8}{10} \) is 8 tenths). So we plot \( 2\frac{4}{5} \) 8 ticks to the right of 2.

Answer:

To plot \( \frac{9}{10} \): 9 ticks to the right of 0 (before 1). To plot \( 2\frac{4}{5} \) (which is \( 2\frac{8}{10} \)): 8 ticks to the right of 2. (Note: The actual plotting is done on the number line as described, with \( \frac{9}{10} \) near 1 (9/10 of the way from 0 to 1) and \( 2\frac{4}{5} \) (2.8) 8/10 of the way from 2 to 3.)